Degree Of Price Discrimination

Presume the single monopoly price is $30 and price elasticity of demand in markets X
and Y are 4 and 10 correspondingly. Determine the Marginal revenues of X and Y.

Solution

MR
in Market X = ARx ex– 1
ex

= 30 4 – 1
4

= 30 * ¾

= 22.5

MR
in Market Y = ARy ey– 1
ey

= 30 10 – 1
10

= 30 * 9/10

= 27

It is therefore unambiguous that marginal revenue in the two markets is varied when
price elasticities of demand at the single monopoly price are diverse. Moreover from
the above, illustration it is obvious that the marginal revenue in the market in which
price elasticity is lesser.

Now, it is profitable
for the monopolist to transfer some volume of the commodity from the market X where
elasticity is low and thus marginal revenue is less to the market Y where elasticity
is low and thus marginal revenue is huge.

In this method the
loss of revenue by decreasing sales in market X by some marginal units will be smaller
than the gain in revenue from enhancing sales in market Y by those units.

Therefore, in the
above illustration, if one unit of commodity is reserved from market X the loss in
income will be $22.5 whilst with the supplementary to sales by one by additional unit
of the commodity in market Y the gain in income will be about $27.

It is unambiguous
that the devolution of some units of the commodity will be profitable when there is
diversity in price elasticities of demand and hence in marginal revenues.

Illustration 86

Presume complete value of price elasticity in market X parities to 4 and in market Y
parities to 6, then

6 – 15Px = 6 = 6
Py 4 – 13
4 4

= 5 * 4
6 3

= 10 / 9

Therefore, when elasticities in markets X and Y are 4 and 6 correspondingly, the prices
in the two markets will be in the ration 10:9.

From the foregoing study it follows that the subsequent two clauses are needed to be
fulfilled for the symmetry of a discriminating monopolist:

Presume a discriminating monopolist is selling a commodity in two diverse markets in
which demand functions are:

R1 = 24 – V1
R2 = 40 – V2

The monopolist’s aggregate cost function is

TC = 6
+ 4V

As an economic adviser you are asked to ascertain the prices to be charged in the two
markets and volume of productivity to be sold in each market so that profits are optimised.
You are also required to compute the aggregate profits to be made from the strategy
of price discrimination. What advice will you provide?

Solution

As profits in case of price discrimination are optimised when MR1 = MR2 = MC. Thus,
we have to compute the marginal revenue in the two markets from the provided demand
functions of the two markets.

Aggregate revenue
in market 1 = R1V1 = 24V1 – V1^2 …..(1)

MR1 in market 1 = Δ(R1V1) = 24 – 2V1
ΔV1

Aggregate revenue
in market 2 = R2V2 = 40V2 – V2^2 …..(2)

MR2 in market 2 = Δ(R2V2) = 40 – 2V2
ΔV2

We can obtain the marginal cost from the aggregate cost function

TC = 6
+ 4V

MC = ΔTC = 4
ΔV

Profit optimising volume of productivity to be sold in the two markets is ascertained
by applying the symmetry condition MR1 = MR2 = MC and solving the following equations:

MR1 = MC

24 – 2V1 = 4

2V1 = 24 – 4

V1 = 20
/ 2

V1 = 10

MR2 = MC

40 – 2V2 = 4

2V2 = 40 – 4

V2 = 36
/ 2

V2 = 18

Substituting these symmetry productivities V1 and V2 in the demand functions we procure
the profit optimising prices:

R1 = 24 – V1 = 24 – 10 = 14

R2 = 40 – V2 = 40 – 18 = 22

Aggregate profits can be procured in the usual method.

Aggregate Profits π = (TR1
+ TR2) – TC

= P1V1
+ P2V2 – (6 + 4V)

= (14*10)
+ (22*18) – [6 + 4(10 +18)]

= 140
+ 396 – 280 = 256

Illustration 88

A developing nation’s monopoly industry sells its commodity in its and to a developed
nation’s markets. The developing nation’s demand function for the commodity
is Ri = 200 – Vi and the US demand function for the commodity is Ru = 160 – 4Vu
where both prices are measured in dollars.

The industry’s marginal cost of commodity is $40 in both the nations. If the developing
nation’s monopoly industry can prevent any resale what price will it charge in
both markets?

Solution

It is to be noted that the markets inverse demand functions are provided such as Ri
= 200 – V1 and Ru = 160 – 4Vu. In order to ascertain the symmetry productivity
prices in the two markets we have to first ascertain the marginal revenue functions
corresponding to the provided linear demand functions.

Moreover, the marginal revenue is twice as sheer as the incline of the linear demand
function. Thus,

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